Abstract

In this work, low thermal-mass LEDs (LTM-LEDs) were developed and demonstrated in flip-chip configuration, studying both experimentally and theoretically the enhanced electrical and optical characteristics and the limits. LTM-LED chips in 25 × 25 μm2, 50 × 50 μm2, 100 × 100 μm2 and 200 × 200 μm2 mesa sizes were fabricated and comparatively investigated. Here it was revealed that both the electrical and optical properties are improved by the decreasing chip size due to the reduced thermal mass. With a smaller chip size (from 200 μm to 50 μm), the device generally presents higher current density against the bias and higher power density against the current density. However, the 25 × 25 μm2 device behaves differently, limited by the fabrication margin limit of 10 μm. The underneath mechanisms of these observations are uncovered, and furthermore, based on the device model, it is proven that for a specific flip-chip fabrication process, the ideal size for LTM-LEDs with optimal power density performance can be identified.

© 2014 Optical Society of America

Full Article  |  PDF Article
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  6. S. T. Tan, X. W. Sun, H. V. Demir, and S. P. DenBaars, “Advances in the LED Materials and Architectures for Energy-Saving Solid-State Lighting Toward “Lighting Revolution”,” IEEE Photon. J. 4(2), 613–619 (2012).
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    [Crossref]
  16. S. X. Jin, J. Shakya, J. Y. Lin, and H. X. Jiang, “Size dependence of III-nitride microdisk light-emitting diode characteristics,” Appl. Phys. Lett. 78(22), 3532–3534 (2001).
    [Crossref]
  17. Z. Gong, H. X. Zhang, E. Gu, C. Griffin, M. D. Dawson, V. Poher, G. Kennedy, P. M. W. French, and M. A. A. Neil, “Matrix-addressable micropixellated InGaN light-emitting diodes with uniform emission and increased light output,” IEEE Trans. Electron. Dev. 54(10), 2650–2658 (2007).
    [Crossref]
  18. Z. Gong, E. Gu, S. R. Jin, D. Massoubre, B. Guilhabert, H. X. Zhang, M. D. Dawson, V. Poher, G. T. Kennedy, P. M. W. French, and M. A. A. Neil, “Efficient flip-chip InGaN micro-pixellated light-emitting diode arrays: Promising candidates for micro-displays and colour conversion,” J. Phys. D Appl. Phys. 41(9), 094002 (2008).
    [Crossref]
  19. H. W. Choi, C. W. Jeon, and M. D. Dawson, “High-resolution 128 x 96 nitride microdisplay,” IEEE Electron Device Lett. 25(5), 277–279 (2004).
    [Crossref]
  20. G. Zheng, S. Jin, C. Yujie, J. McKendry, D. Massoubre, I. M. Watson, E. Gu, and M. D. Dawson, “Size-dependent light output, spectral shift, and self-heating of 400 nm InGaN light-emitting diodes,” J. Appl. Phys. 107(1), 013103 (2010).
    [Crossref]
  21. S. X. Jin, J. Li, J. Z. Li, J. Y. Lin, and H. X. Jiang, “GaN microdisk light emitting diodes,” Appl. Phys. Lett. 76(5), 631–633 (2000).
    [Crossref]
  22. H. P. Zhao, R. A. Arif, Y. K. Ee, and N. Tansu, “Self-Consistent Analysis of Strain-Compensated InGaN-AlGaN Quantum Wells for Lasers and Light-Emitting Diodes,” IEEE J. Quantum Electron. 45(1), 66–78 (2009).
    [Crossref]
  23. M. Meneghini, N. Trivellin, G. Meneghesso, E. Zanoni, U. Zehnder, and B. Hahn, “A combined electro-optical method for the determination of the recombination parameters in InGaN-based light-emitting diodes,” J. Appl. Phys. 106(11), 114508 (2009).
    [Crossref]
  24. V. Fiorentini, F. Bernardini, and O. Ambacher, “Evidence for nonlinear macroscopic polarization in III-V nitride alloy heterostructures,” Appl. Phys. Lett. 80(7), 1204–1206 (2002).
    [Crossref]
  25. J. Piprek and S. Nakamura, “Physics of high-power InGaN/GaN lasers,” IEE Proc., Optoelectron. 149(4), 145–151 (2002).
    [Crossref]
  26. I. Vurgaftman and J. R. Meyer, “Band parameters for nitrogen-containing semiconductors,” J. Appl. Phys. 94(6), 3675–3696 (2003).
    [Crossref]
  27. Z. H. Zhang, S. T. Tan, Z. G. Ju, W. Liu, Y. Ji, Z. Kyaw, Y. Dikme, X. W. Sun, and H. V. Demir, “On the Effect of Step-Doped Quantum Barriers in InGaN/GaN Light Emitting Diodes,” J. Disp. Technol. 9(4), 226–233 (2013).
    [Crossref]
  28. K. A. Bulashevich, I. Y. Evstratov, V. F. Mymrin, and S. Y. Karpov, “Current spreading and thermal effects in blue LED dice,” Phys. Status Solidi C 4(1), 45–48 (2007).
    [Crossref]

2013 (4)

Z. G. Ju, W. Liu, Z. H. Zhang, S. T. Tan, Y. Ji, Z. B. Kyaw, X. L. Zhang, S. P. Lu, Y. P. Zhang, B. B. Zhu, N. Hasanov, X. W. Sun, and H. V. Demir, “Improved hole distribution in InGaN/GaN light-emitting diodes with graded thickness quantum barriers,” Appl. Phys. Lett. 102(24), 243504 (2013).
[Crossref]

Y. Ji, Z. H. Zhang, S. T. Tan, Z. G. Ju, Z. Kyaw, N. Hasanov, W. Liu, X. W. Sun, and H. V. Demir, “Enhanced hole transport in InGaN/GaN multiple quantum well light-emitting diodes with a p-type doped quantum barrier,” Opt. Lett. 38(2), 202–204 (2013).
[Crossref] [PubMed]

Z. H. Zhang, S. T. Tan, W. Liu, Z. G. Ju, K. Zheng, Z. Kyaw, Y. Ji, N. Hasanov, X. W. Sun, and H. V. Demir, “Improved InGaN/GaN light-emitting diodes with a p-GaN/n-GaN/p-GaN/n-GaN/p-GaN current-spreading layer,” Opt. Express 21(4), 4958–4969 (2013).
[PubMed]

Z. H. Zhang, S. T. Tan, Z. G. Ju, W. Liu, Y. Ji, Z. Kyaw, Y. Dikme, X. W. Sun, and H. V. Demir, “On the Effect of Step-Doped Quantum Barriers in InGaN/GaN Light Emitting Diodes,” J. Disp. Technol. 9(4), 226–233 (2013).
[Crossref]

2012 (2)

J. J. D. McKendry, D. Massoubre, S. Zhang, B. R. Rae, R. P. Green, E. Gu, R. K. Henderson, A. E. Kelly, and M. D. Dawson, “Visible-Light Communications Using a CMOS-Controlled Micro-Light- Emitting-Diode Array,” J. Lightwave Technol. 30(1), 61–67 (2012).
[Crossref]

S. T. Tan, X. W. Sun, H. V. Demir, and S. P. DenBaars, “Advances in the LED Materials and Architectures for Energy-Saving Solid-State Lighting Toward “Lighting Revolution”,” IEEE Photon. J. 4(2), 613–619 (2012).
[Crossref]

2011 (1)

R. Haitz and J. Y. Tsao, “Solid-state lighting: ‘The case’ 10 years after and future prospects,” Phys. Status Solidi A 208(1), 17–29 (2011).
[Crossref]

2010 (3)

J. J. D. McKendry, R. P. Green, A. E. Kelly, G. Zheng, B. Guilhabert, D. Massoubre, E. Gu, and M. D. Dawson, “High-Speed Visible Light Communications Using Individual Pixels in a Micro Light-Emitting Diode Array,” IEEE Photonic. Tech. L. 22(18), 1346–1348 (2010).
[Crossref]

J. Pandey, A. Yu-Te Liao, R. Lingley, B. Mirjalili, Parviz, and B. P. Otis, “A Fully Integrated RF-Powered Contact Lens With a Single Element Display,” IEEE Trans Biomed Circuits Syst 4(6), 454–461 (2010).
[Crossref] [PubMed]

G. Zheng, S. Jin, C. Yujie, J. McKendry, D. Massoubre, I. M. Watson, E. Gu, and M. D. Dawson, “Size-dependent light output, spectral shift, and self-heating of 400 nm InGaN light-emitting diodes,” J. Appl. Phys. 107(1), 013103 (2010).
[Crossref]

2009 (4)

H. P. Zhao, R. A. Arif, Y. K. Ee, and N. Tansu, “Self-Consistent Analysis of Strain-Compensated InGaN-AlGaN Quantum Wells for Lasers and Light-Emitting Diodes,” IEEE J. Quantum Electron. 45(1), 66–78 (2009).
[Crossref]

M. Meneghini, N. Trivellin, G. Meneghesso, E. Zanoni, U. Zehnder, and B. Hahn, “A combined electro-optical method for the determination of the recombination parameters in InGaN-based light-emitting diodes,” J. Appl. Phys. 106(11), 114508 (2009).
[Crossref]

I. L. Azevedo, M. G. Morgan, and F. Morgan, “The Transition to Solid-State Lighting,” Proc. IEEE 97(3), 481–510 (2009).
[Crossref]

M. H. Crawford, “LEDs for Solid-State Lighting: Performance Challenges and Recent Advances,” IEEE J. Sel. Top. Quant. 15(4), 1028–1040 (2009).
[Crossref]

2008 (2)

V. Poher, N. Grossman, G. T. Kennedy, K. Nikolic, H. X. Zhang, Z. Gong, E. M. Drakakis, E. Gu, M. D. Dawson, P. M. W. French, P. Degenaar, and M. A. A. Neil, “Micro-LED arrays: a tool for two-dimensional neuron stimulation,” J. Phys. D Appl. Phys. 41(9), 094014 (2008).
[Crossref]

Z. Gong, E. Gu, S. R. Jin, D. Massoubre, B. Guilhabert, H. X. Zhang, M. D. Dawson, V. Poher, G. T. Kennedy, P. M. W. French, and M. A. A. Neil, “Efficient flip-chip InGaN micro-pixellated light-emitting diode arrays: Promising candidates for micro-displays and colour conversion,” J. Phys. D Appl. Phys. 41(9), 094002 (2008).
[Crossref]

2007 (3)

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, Z. Ling, G. Harbers, and M. G. Craford, “Status and Future of High-Power Light-Emitting Diodes for Solid-State Lighting,” J. Disp. Technol. 3(2), 160–175 (2007).
[Crossref]

Z. Gong, H. X. Zhang, E. Gu, C. Griffin, M. D. Dawson, V. Poher, G. Kennedy, P. M. W. French, and M. A. A. Neil, “Matrix-addressable micropixellated InGaN light-emitting diodes with uniform emission and increased light output,” IEEE Trans. Electron. Dev. 54(10), 2650–2658 (2007).
[Crossref]

K. A. Bulashevich, I. Y. Evstratov, V. F. Mymrin, and S. Y. Karpov, “Current spreading and thermal effects in blue LED dice,” Phys. Status Solidi C 4(1), 45–48 (2007).
[Crossref]

2004 (2)

H. W. Choi, C. W. Jeon, and M. D. Dawson, “InGaN microring light-emitting diodes,” IEEE Photonic. Tech. L. 16(1), 33–35 (2004).
[Crossref]

H. W. Choi, C. W. Jeon, and M. D. Dawson, “High-resolution 128 x 96 nitride microdisplay,” IEEE Electron Device Lett. 25(5), 277–279 (2004).
[Crossref]

2003 (2)

H. W. Choi, M. D. Dawson, P. R. Edwards, and R. W. Martin, “High extraction efficiency InGaN micro-ring light-emitting diodes,” Appl. Phys. Lett. 83(22), 4483–4485 (2003).
[Crossref]

I. Vurgaftman and J. R. Meyer, “Band parameters for nitrogen-containing semiconductors,” J. Appl. Phys. 94(6), 3675–3696 (2003).
[Crossref]

2002 (2)

V. Fiorentini, F. Bernardini, and O. Ambacher, “Evidence for nonlinear macroscopic polarization in III-V nitride alloy heterostructures,” Appl. Phys. Lett. 80(7), 1204–1206 (2002).
[Crossref]

J. Piprek and S. Nakamura, “Physics of high-power InGaN/GaN lasers,” IEE Proc., Optoelectron. 149(4), 145–151 (2002).
[Crossref]

2001 (2)

S. X. Jin, J. Shakya, J. Y. Lin, and H. X. Jiang, “Size dependence of III-nitride microdisk light-emitting diode characteristics,” Appl. Phys. Lett. 78(22), 3532–3534 (2001).
[Crossref]

A. Bergh, G. Craford, A. Duggal, and R. Haitz, “The promise and challenge of solid-state lighting,” Phys. Today 54(12), 42–47 (2001).
[Crossref]

2000 (1)

S. X. Jin, J. Li, J. Z. Li, J. Y. Lin, and H. X. Jiang, “GaN microdisk light emitting diodes,” Appl. Phys. Lett. 76(5), 631–633 (2000).
[Crossref]

Ambacher, O.

V. Fiorentini, F. Bernardini, and O. Ambacher, “Evidence for nonlinear macroscopic polarization in III-V nitride alloy heterostructures,” Appl. Phys. Lett. 80(7), 1204–1206 (2002).
[Crossref]

Arif, R. A.

H. P. Zhao, R. A. Arif, Y. K. Ee, and N. Tansu, “Self-Consistent Analysis of Strain-Compensated InGaN-AlGaN Quantum Wells for Lasers and Light-Emitting Diodes,” IEEE J. Quantum Electron. 45(1), 66–78 (2009).
[Crossref]

Azevedo, I. L.

I. L. Azevedo, M. G. Morgan, and F. Morgan, “The Transition to Solid-State Lighting,” Proc. IEEE 97(3), 481–510 (2009).
[Crossref]

Bergh, A.

A. Bergh, G. Craford, A. Duggal, and R. Haitz, “The promise and challenge of solid-state lighting,” Phys. Today 54(12), 42–47 (2001).
[Crossref]

Bernardini, F.

V. Fiorentini, F. Bernardini, and O. Ambacher, “Evidence for nonlinear macroscopic polarization in III-V nitride alloy heterostructures,” Appl. Phys. Lett. 80(7), 1204–1206 (2002).
[Crossref]

Bulashevich, K. A.

K. A. Bulashevich, I. Y. Evstratov, V. F. Mymrin, and S. Y. Karpov, “Current spreading and thermal effects in blue LED dice,” Phys. Status Solidi C 4(1), 45–48 (2007).
[Crossref]

Choi, H. W.

H. W. Choi, C. W. Jeon, and M. D. Dawson, “High-resolution 128 x 96 nitride microdisplay,” IEEE Electron Device Lett. 25(5), 277–279 (2004).
[Crossref]

H. W. Choi, C. W. Jeon, and M. D. Dawson, “InGaN microring light-emitting diodes,” IEEE Photonic. Tech. L. 16(1), 33–35 (2004).
[Crossref]

H. W. Choi, M. D. Dawson, P. R. Edwards, and R. W. Martin, “High extraction efficiency InGaN micro-ring light-emitting diodes,” Appl. Phys. Lett. 83(22), 4483–4485 (2003).
[Crossref]

Craford, G.

A. Bergh, G. Craford, A. Duggal, and R. Haitz, “The promise and challenge of solid-state lighting,” Phys. Today 54(12), 42–47 (2001).
[Crossref]

Craford, M. G.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, Z. Ling, G. Harbers, and M. G. Craford, “Status and Future of High-Power Light-Emitting Diodes for Solid-State Lighting,” J. Disp. Technol. 3(2), 160–175 (2007).
[Crossref]

Crawford, M. H.

M. H. Crawford, “LEDs for Solid-State Lighting: Performance Challenges and Recent Advances,” IEEE J. Sel. Top. Quant. 15(4), 1028–1040 (2009).
[Crossref]

Dawson, M. D.

J. J. D. McKendry, D. Massoubre, S. Zhang, B. R. Rae, R. P. Green, E. Gu, R. K. Henderson, A. E. Kelly, and M. D. Dawson, “Visible-Light Communications Using a CMOS-Controlled Micro-Light- Emitting-Diode Array,” J. Lightwave Technol. 30(1), 61–67 (2012).
[Crossref]

J. J. D. McKendry, R. P. Green, A. E. Kelly, G. Zheng, B. Guilhabert, D. Massoubre, E. Gu, and M. D. Dawson, “High-Speed Visible Light Communications Using Individual Pixels in a Micro Light-Emitting Diode Array,” IEEE Photonic. Tech. L. 22(18), 1346–1348 (2010).
[Crossref]

G. Zheng, S. Jin, C. Yujie, J. McKendry, D. Massoubre, I. M. Watson, E. Gu, and M. D. Dawson, “Size-dependent light output, spectral shift, and self-heating of 400 nm InGaN light-emitting diodes,” J. Appl. Phys. 107(1), 013103 (2010).
[Crossref]

Z. Gong, E. Gu, S. R. Jin, D. Massoubre, B. Guilhabert, H. X. Zhang, M. D. Dawson, V. Poher, G. T. Kennedy, P. M. W. French, and M. A. A. Neil, “Efficient flip-chip InGaN micro-pixellated light-emitting diode arrays: Promising candidates for micro-displays and colour conversion,” J. Phys. D Appl. Phys. 41(9), 094002 (2008).
[Crossref]

V. Poher, N. Grossman, G. T. Kennedy, K. Nikolic, H. X. Zhang, Z. Gong, E. M. Drakakis, E. Gu, M. D. Dawson, P. M. W. French, P. Degenaar, and M. A. A. Neil, “Micro-LED arrays: a tool for two-dimensional neuron stimulation,” J. Phys. D Appl. Phys. 41(9), 094014 (2008).
[Crossref]

Z. Gong, H. X. Zhang, E. Gu, C. Griffin, M. D. Dawson, V. Poher, G. Kennedy, P. M. W. French, and M. A. A. Neil, “Matrix-addressable micropixellated InGaN light-emitting diodes with uniform emission and increased light output,” IEEE Trans. Electron. Dev. 54(10), 2650–2658 (2007).
[Crossref]

H. W. Choi, C. W. Jeon, and M. D. Dawson, “High-resolution 128 x 96 nitride microdisplay,” IEEE Electron Device Lett. 25(5), 277–279 (2004).
[Crossref]

H. W. Choi, C. W. Jeon, and M. D. Dawson, “InGaN microring light-emitting diodes,” IEEE Photonic. Tech. L. 16(1), 33–35 (2004).
[Crossref]

H. W. Choi, M. D. Dawson, P. R. Edwards, and R. W. Martin, “High extraction efficiency InGaN micro-ring light-emitting diodes,” Appl. Phys. Lett. 83(22), 4483–4485 (2003).
[Crossref]

Degenaar, P.

V. Poher, N. Grossman, G. T. Kennedy, K. Nikolic, H. X. Zhang, Z. Gong, E. M. Drakakis, E. Gu, M. D. Dawson, P. M. W. French, P. Degenaar, and M. A. A. Neil, “Micro-LED arrays: a tool for two-dimensional neuron stimulation,” J. Phys. D Appl. Phys. 41(9), 094014 (2008).
[Crossref]

Demir, H. V.

Z. G. Ju, W. Liu, Z. H. Zhang, S. T. Tan, Y. Ji, Z. B. Kyaw, X. L. Zhang, S. P. Lu, Y. P. Zhang, B. B. Zhu, N. Hasanov, X. W. Sun, and H. V. Demir, “Improved hole distribution in InGaN/GaN light-emitting diodes with graded thickness quantum barriers,” Appl. Phys. Lett. 102(24), 243504 (2013).
[Crossref]

Z. H. Zhang, S. T. Tan, Z. G. Ju, W. Liu, Y. Ji, Z. Kyaw, Y. Dikme, X. W. Sun, and H. V. Demir, “On the Effect of Step-Doped Quantum Barriers in InGaN/GaN Light Emitting Diodes,” J. Disp. Technol. 9(4), 226–233 (2013).
[Crossref]

Y. Ji, Z. H. Zhang, S. T. Tan, Z. G. Ju, Z. Kyaw, N. Hasanov, W. Liu, X. W. Sun, and H. V. Demir, “Enhanced hole transport in InGaN/GaN multiple quantum well light-emitting diodes with a p-type doped quantum barrier,” Opt. Lett. 38(2), 202–204 (2013).
[Crossref] [PubMed]

Z. H. Zhang, S. T. Tan, W. Liu, Z. G. Ju, K. Zheng, Z. Kyaw, Y. Ji, N. Hasanov, X. W. Sun, and H. V. Demir, “Improved InGaN/GaN light-emitting diodes with a p-GaN/n-GaN/p-GaN/n-GaN/p-GaN current-spreading layer,” Opt. Express 21(4), 4958–4969 (2013).
[PubMed]

S. T. Tan, X. W. Sun, H. V. Demir, and S. P. DenBaars, “Advances in the LED Materials and Architectures for Energy-Saving Solid-State Lighting Toward “Lighting Revolution”,” IEEE Photon. J. 4(2), 613–619 (2012).
[Crossref]

DenBaars, S. P.

S. T. Tan, X. W. Sun, H. V. Demir, and S. P. DenBaars, “Advances in the LED Materials and Architectures for Energy-Saving Solid-State Lighting Toward “Lighting Revolution”,” IEEE Photon. J. 4(2), 613–619 (2012).
[Crossref]

Dikme, Y.

Z. H. Zhang, S. T. Tan, Z. G. Ju, W. Liu, Y. Ji, Z. Kyaw, Y. Dikme, X. W. Sun, and H. V. Demir, “On the Effect of Step-Doped Quantum Barriers in InGaN/GaN Light Emitting Diodes,” J. Disp. Technol. 9(4), 226–233 (2013).
[Crossref]

Drakakis, E. M.

V. Poher, N. Grossman, G. T. Kennedy, K. Nikolic, H. X. Zhang, Z. Gong, E. M. Drakakis, E. Gu, M. D. Dawson, P. M. W. French, P. Degenaar, and M. A. A. Neil, “Micro-LED arrays: a tool for two-dimensional neuron stimulation,” J. Phys. D Appl. Phys. 41(9), 094014 (2008).
[Crossref]

Duggal, A.

A. Bergh, G. Craford, A. Duggal, and R. Haitz, “The promise and challenge of solid-state lighting,” Phys. Today 54(12), 42–47 (2001).
[Crossref]

Edwards, P. R.

H. W. Choi, M. D. Dawson, P. R. Edwards, and R. W. Martin, “High extraction efficiency InGaN micro-ring light-emitting diodes,” Appl. Phys. Lett. 83(22), 4483–4485 (2003).
[Crossref]

Ee, Y. K.

H. P. Zhao, R. A. Arif, Y. K. Ee, and N. Tansu, “Self-Consistent Analysis of Strain-Compensated InGaN-AlGaN Quantum Wells for Lasers and Light-Emitting Diodes,” IEEE J. Quantum Electron. 45(1), 66–78 (2009).
[Crossref]

Evstratov, I. Y.

K. A. Bulashevich, I. Y. Evstratov, V. F. Mymrin, and S. Y. Karpov, “Current spreading and thermal effects in blue LED dice,” Phys. Status Solidi C 4(1), 45–48 (2007).
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Fiorentini, V.

V. Fiorentini, F. Bernardini, and O. Ambacher, “Evidence for nonlinear macroscopic polarization in III-V nitride alloy heterostructures,” Appl. Phys. Lett. 80(7), 1204–1206 (2002).
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French, P. M. W.

Z. Gong, E. Gu, S. R. Jin, D. Massoubre, B. Guilhabert, H. X. Zhang, M. D. Dawson, V. Poher, G. T. Kennedy, P. M. W. French, and M. A. A. Neil, “Efficient flip-chip InGaN micro-pixellated light-emitting diode arrays: Promising candidates for micro-displays and colour conversion,” J. Phys. D Appl. Phys. 41(9), 094002 (2008).
[Crossref]

V. Poher, N. Grossman, G. T. Kennedy, K. Nikolic, H. X. Zhang, Z. Gong, E. M. Drakakis, E. Gu, M. D. Dawson, P. M. W. French, P. Degenaar, and M. A. A. Neil, “Micro-LED arrays: a tool for two-dimensional neuron stimulation,” J. Phys. D Appl. Phys. 41(9), 094014 (2008).
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Z. Gong, H. X. Zhang, E. Gu, C. Griffin, M. D. Dawson, V. Poher, G. Kennedy, P. M. W. French, and M. A. A. Neil, “Matrix-addressable micropixellated InGaN light-emitting diodes with uniform emission and increased light output,” IEEE Trans. Electron. Dev. 54(10), 2650–2658 (2007).
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Gong, Z.

Z. Gong, E. Gu, S. R. Jin, D. Massoubre, B. Guilhabert, H. X. Zhang, M. D. Dawson, V. Poher, G. T. Kennedy, P. M. W. French, and M. A. A. Neil, “Efficient flip-chip InGaN micro-pixellated light-emitting diode arrays: Promising candidates for micro-displays and colour conversion,” J. Phys. D Appl. Phys. 41(9), 094002 (2008).
[Crossref]

V. Poher, N. Grossman, G. T. Kennedy, K. Nikolic, H. X. Zhang, Z. Gong, E. M. Drakakis, E. Gu, M. D. Dawson, P. M. W. French, P. Degenaar, and M. A. A. Neil, “Micro-LED arrays: a tool for two-dimensional neuron stimulation,” J. Phys. D Appl. Phys. 41(9), 094014 (2008).
[Crossref]

Z. Gong, H. X. Zhang, E. Gu, C. Griffin, M. D. Dawson, V. Poher, G. Kennedy, P. M. W. French, and M. A. A. Neil, “Matrix-addressable micropixellated InGaN light-emitting diodes with uniform emission and increased light output,” IEEE Trans. Electron. Dev. 54(10), 2650–2658 (2007).
[Crossref]

Green, R. P.

J. J. D. McKendry, D. Massoubre, S. Zhang, B. R. Rae, R. P. Green, E. Gu, R. K. Henderson, A. E. Kelly, and M. D. Dawson, “Visible-Light Communications Using a CMOS-Controlled Micro-Light- Emitting-Diode Array,” J. Lightwave Technol. 30(1), 61–67 (2012).
[Crossref]

J. J. D. McKendry, R. P. Green, A. E. Kelly, G. Zheng, B. Guilhabert, D. Massoubre, E. Gu, and M. D. Dawson, “High-Speed Visible Light Communications Using Individual Pixels in a Micro Light-Emitting Diode Array,” IEEE Photonic. Tech. L. 22(18), 1346–1348 (2010).
[Crossref]

Griffin, C.

Z. Gong, H. X. Zhang, E. Gu, C. Griffin, M. D. Dawson, V. Poher, G. Kennedy, P. M. W. French, and M. A. A. Neil, “Matrix-addressable micropixellated InGaN light-emitting diodes with uniform emission and increased light output,” IEEE Trans. Electron. Dev. 54(10), 2650–2658 (2007).
[Crossref]

Grossman, N.

V. Poher, N. Grossman, G. T. Kennedy, K. Nikolic, H. X. Zhang, Z. Gong, E. M. Drakakis, E. Gu, M. D. Dawson, P. M. W. French, P. Degenaar, and M. A. A. Neil, “Micro-LED arrays: a tool for two-dimensional neuron stimulation,” J. Phys. D Appl. Phys. 41(9), 094014 (2008).
[Crossref]

Gu, E.

J. J. D. McKendry, D. Massoubre, S. Zhang, B. R. Rae, R. P. Green, E. Gu, R. K. Henderson, A. E. Kelly, and M. D. Dawson, “Visible-Light Communications Using a CMOS-Controlled Micro-Light- Emitting-Diode Array,” J. Lightwave Technol. 30(1), 61–67 (2012).
[Crossref]

J. J. D. McKendry, R. P. Green, A. E. Kelly, G. Zheng, B. Guilhabert, D. Massoubre, E. Gu, and M. D. Dawson, “High-Speed Visible Light Communications Using Individual Pixels in a Micro Light-Emitting Diode Array,” IEEE Photonic. Tech. L. 22(18), 1346–1348 (2010).
[Crossref]

G. Zheng, S. Jin, C. Yujie, J. McKendry, D. Massoubre, I. M. Watson, E. Gu, and M. D. Dawson, “Size-dependent light output, spectral shift, and self-heating of 400 nm InGaN light-emitting diodes,” J. Appl. Phys. 107(1), 013103 (2010).
[Crossref]

Z. Gong, E. Gu, S. R. Jin, D. Massoubre, B. Guilhabert, H. X. Zhang, M. D. Dawson, V. Poher, G. T. Kennedy, P. M. W. French, and M. A. A. Neil, “Efficient flip-chip InGaN micro-pixellated light-emitting diode arrays: Promising candidates for micro-displays and colour conversion,” J. Phys. D Appl. Phys. 41(9), 094002 (2008).
[Crossref]

V. Poher, N. Grossman, G. T. Kennedy, K. Nikolic, H. X. Zhang, Z. Gong, E. M. Drakakis, E. Gu, M. D. Dawson, P. M. W. French, P. Degenaar, and M. A. A. Neil, “Micro-LED arrays: a tool for two-dimensional neuron stimulation,” J. Phys. D Appl. Phys. 41(9), 094014 (2008).
[Crossref]

Z. Gong, H. X. Zhang, E. Gu, C. Griffin, M. D. Dawson, V. Poher, G. Kennedy, P. M. W. French, and M. A. A. Neil, “Matrix-addressable micropixellated InGaN light-emitting diodes with uniform emission and increased light output,” IEEE Trans. Electron. Dev. 54(10), 2650–2658 (2007).
[Crossref]

Guilhabert, B.

J. J. D. McKendry, R. P. Green, A. E. Kelly, G. Zheng, B. Guilhabert, D. Massoubre, E. Gu, and M. D. Dawson, “High-Speed Visible Light Communications Using Individual Pixels in a Micro Light-Emitting Diode Array,” IEEE Photonic. Tech. L. 22(18), 1346–1348 (2010).
[Crossref]

Z. Gong, E. Gu, S. R. Jin, D. Massoubre, B. Guilhabert, H. X. Zhang, M. D. Dawson, V. Poher, G. T. Kennedy, P. M. W. French, and M. A. A. Neil, “Efficient flip-chip InGaN micro-pixellated light-emitting diode arrays: Promising candidates for micro-displays and colour conversion,” J. Phys. D Appl. Phys. 41(9), 094002 (2008).
[Crossref]

Hahn, B.

M. Meneghini, N. Trivellin, G. Meneghesso, E. Zanoni, U. Zehnder, and B. Hahn, “A combined electro-optical method for the determination of the recombination parameters in InGaN-based light-emitting diodes,” J. Appl. Phys. 106(11), 114508 (2009).
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Haitz, R.

R. Haitz and J. Y. Tsao, “Solid-state lighting: ‘The case’ 10 years after and future prospects,” Phys. Status Solidi A 208(1), 17–29 (2011).
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A. Bergh, G. Craford, A. Duggal, and R. Haitz, “The promise and challenge of solid-state lighting,” Phys. Today 54(12), 42–47 (2001).
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Harbers, G.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, Z. Ling, G. Harbers, and M. G. Craford, “Status and Future of High-Power Light-Emitting Diodes for Solid-State Lighting,” J. Disp. Technol. 3(2), 160–175 (2007).
[Crossref]

Hasanov, N.

Henderson, R. K.

Jeon, C. W.

H. W. Choi, C. W. Jeon, and M. D. Dawson, “InGaN microring light-emitting diodes,” IEEE Photonic. Tech. L. 16(1), 33–35 (2004).
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H. W. Choi, C. W. Jeon, and M. D. Dawson, “High-resolution 128 x 96 nitride microdisplay,” IEEE Electron Device Lett. 25(5), 277–279 (2004).
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Ji, Y.

Z. H. Zhang, S. T. Tan, Z. G. Ju, W. Liu, Y. Ji, Z. Kyaw, Y. Dikme, X. W. Sun, and H. V. Demir, “On the Effect of Step-Doped Quantum Barriers in InGaN/GaN Light Emitting Diodes,” J. Disp. Technol. 9(4), 226–233 (2013).
[Crossref]

Z. G. Ju, W. Liu, Z. H. Zhang, S. T. Tan, Y. Ji, Z. B. Kyaw, X. L. Zhang, S. P. Lu, Y. P. Zhang, B. B. Zhu, N. Hasanov, X. W. Sun, and H. V. Demir, “Improved hole distribution in InGaN/GaN light-emitting diodes with graded thickness quantum barriers,” Appl. Phys. Lett. 102(24), 243504 (2013).
[Crossref]

Y. Ji, Z. H. Zhang, S. T. Tan, Z. G. Ju, Z. Kyaw, N. Hasanov, W. Liu, X. W. Sun, and H. V. Demir, “Enhanced hole transport in InGaN/GaN multiple quantum well light-emitting diodes with a p-type doped quantum barrier,” Opt. Lett. 38(2), 202–204 (2013).
[Crossref] [PubMed]

Z. H. Zhang, S. T. Tan, W. Liu, Z. G. Ju, K. Zheng, Z. Kyaw, Y. Ji, N. Hasanov, X. W. Sun, and H. V. Demir, “Improved InGaN/GaN light-emitting diodes with a p-GaN/n-GaN/p-GaN/n-GaN/p-GaN current-spreading layer,” Opt. Express 21(4), 4958–4969 (2013).
[PubMed]

Jiang, H. X.

S. X. Jin, J. Shakya, J. Y. Lin, and H. X. Jiang, “Size dependence of III-nitride microdisk light-emitting diode characteristics,” Appl. Phys. Lett. 78(22), 3532–3534 (2001).
[Crossref]

S. X. Jin, J. Li, J. Z. Li, J. Y. Lin, and H. X. Jiang, “GaN microdisk light emitting diodes,” Appl. Phys. Lett. 76(5), 631–633 (2000).
[Crossref]

Jin, S.

G. Zheng, S. Jin, C. Yujie, J. McKendry, D. Massoubre, I. M. Watson, E. Gu, and M. D. Dawson, “Size-dependent light output, spectral shift, and self-heating of 400 nm InGaN light-emitting diodes,” J. Appl. Phys. 107(1), 013103 (2010).
[Crossref]

Jin, S. R.

Z. Gong, E. Gu, S. R. Jin, D. Massoubre, B. Guilhabert, H. X. Zhang, M. D. Dawson, V. Poher, G. T. Kennedy, P. M. W. French, and M. A. A. Neil, “Efficient flip-chip InGaN micro-pixellated light-emitting diode arrays: Promising candidates for micro-displays and colour conversion,” J. Phys. D Appl. Phys. 41(9), 094002 (2008).
[Crossref]

Jin, S. X.

S. X. Jin, J. Shakya, J. Y. Lin, and H. X. Jiang, “Size dependence of III-nitride microdisk light-emitting diode characteristics,” Appl. Phys. Lett. 78(22), 3532–3534 (2001).
[Crossref]

S. X. Jin, J. Li, J. Z. Li, J. Y. Lin, and H. X. Jiang, “GaN microdisk light emitting diodes,” Appl. Phys. Lett. 76(5), 631–633 (2000).
[Crossref]

Ju, Z. G.

Z. H. Zhang, S. T. Tan, Z. G. Ju, W. Liu, Y. Ji, Z. Kyaw, Y. Dikme, X. W. Sun, and H. V. Demir, “On the Effect of Step-Doped Quantum Barriers in InGaN/GaN Light Emitting Diodes,” J. Disp. Technol. 9(4), 226–233 (2013).
[Crossref]

Z. G. Ju, W. Liu, Z. H. Zhang, S. T. Tan, Y. Ji, Z. B. Kyaw, X. L. Zhang, S. P. Lu, Y. P. Zhang, B. B. Zhu, N. Hasanov, X. W. Sun, and H. V. Demir, “Improved hole distribution in InGaN/GaN light-emitting diodes with graded thickness quantum barriers,” Appl. Phys. Lett. 102(24), 243504 (2013).
[Crossref]

Z. H. Zhang, S. T. Tan, W. Liu, Z. G. Ju, K. Zheng, Z. Kyaw, Y. Ji, N. Hasanov, X. W. Sun, and H. V. Demir, “Improved InGaN/GaN light-emitting diodes with a p-GaN/n-GaN/p-GaN/n-GaN/p-GaN current-spreading layer,” Opt. Express 21(4), 4958–4969 (2013).
[PubMed]

Y. Ji, Z. H. Zhang, S. T. Tan, Z. G. Ju, Z. Kyaw, N. Hasanov, W. Liu, X. W. Sun, and H. V. Demir, “Enhanced hole transport in InGaN/GaN multiple quantum well light-emitting diodes with a p-type doped quantum barrier,” Opt. Lett. 38(2), 202–204 (2013).
[Crossref] [PubMed]

Karpov, S. Y.

K. A. Bulashevich, I. Y. Evstratov, V. F. Mymrin, and S. Y. Karpov, “Current spreading and thermal effects in blue LED dice,” Phys. Status Solidi C 4(1), 45–48 (2007).
[Crossref]

Kelly, A. E.

J. J. D. McKendry, D. Massoubre, S. Zhang, B. R. Rae, R. P. Green, E. Gu, R. K. Henderson, A. E. Kelly, and M. D. Dawson, “Visible-Light Communications Using a CMOS-Controlled Micro-Light- Emitting-Diode Array,” J. Lightwave Technol. 30(1), 61–67 (2012).
[Crossref]

J. J. D. McKendry, R. P. Green, A. E. Kelly, G. Zheng, B. Guilhabert, D. Massoubre, E. Gu, and M. D. Dawson, “High-Speed Visible Light Communications Using Individual Pixels in a Micro Light-Emitting Diode Array,” IEEE Photonic. Tech. L. 22(18), 1346–1348 (2010).
[Crossref]

Kennedy, G.

Z. Gong, H. X. Zhang, E. Gu, C. Griffin, M. D. Dawson, V. Poher, G. Kennedy, P. M. W. French, and M. A. A. Neil, “Matrix-addressable micropixellated InGaN light-emitting diodes with uniform emission and increased light output,” IEEE Trans. Electron. Dev. 54(10), 2650–2658 (2007).
[Crossref]

Kennedy, G. T.

Z. Gong, E. Gu, S. R. Jin, D. Massoubre, B. Guilhabert, H. X. Zhang, M. D. Dawson, V. Poher, G. T. Kennedy, P. M. W. French, and M. A. A. Neil, “Efficient flip-chip InGaN micro-pixellated light-emitting diode arrays: Promising candidates for micro-displays and colour conversion,” J. Phys. D Appl. Phys. 41(9), 094002 (2008).
[Crossref]

V. Poher, N. Grossman, G. T. Kennedy, K. Nikolic, H. X. Zhang, Z. Gong, E. M. Drakakis, E. Gu, M. D. Dawson, P. M. W. French, P. Degenaar, and M. A. A. Neil, “Micro-LED arrays: a tool for two-dimensional neuron stimulation,” J. Phys. D Appl. Phys. 41(9), 094014 (2008).
[Crossref]

Krames, M. R.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, Z. Ling, G. Harbers, and M. G. Craford, “Status and Future of High-Power Light-Emitting Diodes for Solid-State Lighting,” J. Disp. Technol. 3(2), 160–175 (2007).
[Crossref]

Kyaw, Z.

Kyaw, Z. B.

Z. G. Ju, W. Liu, Z. H. Zhang, S. T. Tan, Y. Ji, Z. B. Kyaw, X. L. Zhang, S. P. Lu, Y. P. Zhang, B. B. Zhu, N. Hasanov, X. W. Sun, and H. V. Demir, “Improved hole distribution in InGaN/GaN light-emitting diodes with graded thickness quantum barriers,” Appl. Phys. Lett. 102(24), 243504 (2013).
[Crossref]

Li, J.

S. X. Jin, J. Li, J. Z. Li, J. Y. Lin, and H. X. Jiang, “GaN microdisk light emitting diodes,” Appl. Phys. Lett. 76(5), 631–633 (2000).
[Crossref]

Li, J. Z.

S. X. Jin, J. Li, J. Z. Li, J. Y. Lin, and H. X. Jiang, “GaN microdisk light emitting diodes,” Appl. Phys. Lett. 76(5), 631–633 (2000).
[Crossref]

Lin, J. Y.

S. X. Jin, J. Shakya, J. Y. Lin, and H. X. Jiang, “Size dependence of III-nitride microdisk light-emitting diode characteristics,” Appl. Phys. Lett. 78(22), 3532–3534 (2001).
[Crossref]

S. X. Jin, J. Li, J. Z. Li, J. Y. Lin, and H. X. Jiang, “GaN microdisk light emitting diodes,” Appl. Phys. Lett. 76(5), 631–633 (2000).
[Crossref]

Ling, Z.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, Z. Ling, G. Harbers, and M. G. Craford, “Status and Future of High-Power Light-Emitting Diodes for Solid-State Lighting,” J. Disp. Technol. 3(2), 160–175 (2007).
[Crossref]

Lingley, R.

J. Pandey, A. Yu-Te Liao, R. Lingley, B. Mirjalili, Parviz, and B. P. Otis, “A Fully Integrated RF-Powered Contact Lens With a Single Element Display,” IEEE Trans Biomed Circuits Syst 4(6), 454–461 (2010).
[Crossref] [PubMed]

Liu, W.

Z. G. Ju, W. Liu, Z. H. Zhang, S. T. Tan, Y. Ji, Z. B. Kyaw, X. L. Zhang, S. P. Lu, Y. P. Zhang, B. B. Zhu, N. Hasanov, X. W. Sun, and H. V. Demir, “Improved hole distribution in InGaN/GaN light-emitting diodes with graded thickness quantum barriers,” Appl. Phys. Lett. 102(24), 243504 (2013).
[Crossref]

Z. H. Zhang, S. T. Tan, Z. G. Ju, W. Liu, Y. Ji, Z. Kyaw, Y. Dikme, X. W. Sun, and H. V. Demir, “On the Effect of Step-Doped Quantum Barriers in InGaN/GaN Light Emitting Diodes,” J. Disp. Technol. 9(4), 226–233 (2013).
[Crossref]

Y. Ji, Z. H. Zhang, S. T. Tan, Z. G. Ju, Z. Kyaw, N. Hasanov, W. Liu, X. W. Sun, and H. V. Demir, “Enhanced hole transport in InGaN/GaN multiple quantum well light-emitting diodes with a p-type doped quantum barrier,” Opt. Lett. 38(2), 202–204 (2013).
[Crossref] [PubMed]

Z. H. Zhang, S. T. Tan, W. Liu, Z. G. Ju, K. Zheng, Z. Kyaw, Y. Ji, N. Hasanov, X. W. Sun, and H. V. Demir, “Improved InGaN/GaN light-emitting diodes with a p-GaN/n-GaN/p-GaN/n-GaN/p-GaN current-spreading layer,” Opt. Express 21(4), 4958–4969 (2013).
[PubMed]

Lu, S. P.

Z. G. Ju, W. Liu, Z. H. Zhang, S. T. Tan, Y. Ji, Z. B. Kyaw, X. L. Zhang, S. P. Lu, Y. P. Zhang, B. B. Zhu, N. Hasanov, X. W. Sun, and H. V. Demir, “Improved hole distribution in InGaN/GaN light-emitting diodes with graded thickness quantum barriers,” Appl. Phys. Lett. 102(24), 243504 (2013).
[Crossref]

Martin, R. W.

H. W. Choi, M. D. Dawson, P. R. Edwards, and R. W. Martin, “High extraction efficiency InGaN micro-ring light-emitting diodes,” Appl. Phys. Lett. 83(22), 4483–4485 (2003).
[Crossref]

Massoubre, D.

J. J. D. McKendry, D. Massoubre, S. Zhang, B. R. Rae, R. P. Green, E. Gu, R. K. Henderson, A. E. Kelly, and M. D. Dawson, “Visible-Light Communications Using a CMOS-Controlled Micro-Light- Emitting-Diode Array,” J. Lightwave Technol. 30(1), 61–67 (2012).
[Crossref]

G. Zheng, S. Jin, C. Yujie, J. McKendry, D. Massoubre, I. M. Watson, E. Gu, and M. D. Dawson, “Size-dependent light output, spectral shift, and self-heating of 400 nm InGaN light-emitting diodes,” J. Appl. Phys. 107(1), 013103 (2010).
[Crossref]

J. J. D. McKendry, R. P. Green, A. E. Kelly, G. Zheng, B. Guilhabert, D. Massoubre, E. Gu, and M. D. Dawson, “High-Speed Visible Light Communications Using Individual Pixels in a Micro Light-Emitting Diode Array,” IEEE Photonic. Tech. L. 22(18), 1346–1348 (2010).
[Crossref]

Z. Gong, E. Gu, S. R. Jin, D. Massoubre, B. Guilhabert, H. X. Zhang, M. D. Dawson, V. Poher, G. T. Kennedy, P. M. W. French, and M. A. A. Neil, “Efficient flip-chip InGaN micro-pixellated light-emitting diode arrays: Promising candidates for micro-displays and colour conversion,” J. Phys. D Appl. Phys. 41(9), 094002 (2008).
[Crossref]

McKendry, J.

G. Zheng, S. Jin, C. Yujie, J. McKendry, D. Massoubre, I. M. Watson, E. Gu, and M. D. Dawson, “Size-dependent light output, spectral shift, and self-heating of 400 nm InGaN light-emitting diodes,” J. Appl. Phys. 107(1), 013103 (2010).
[Crossref]

McKendry, J. J. D.

J. J. D. McKendry, D. Massoubre, S. Zhang, B. R. Rae, R. P. Green, E. Gu, R. K. Henderson, A. E. Kelly, and M. D. Dawson, “Visible-Light Communications Using a CMOS-Controlled Micro-Light- Emitting-Diode Array,” J. Lightwave Technol. 30(1), 61–67 (2012).
[Crossref]

J. J. D. McKendry, R. P. Green, A. E. Kelly, G. Zheng, B. Guilhabert, D. Massoubre, E. Gu, and M. D. Dawson, “High-Speed Visible Light Communications Using Individual Pixels in a Micro Light-Emitting Diode Array,” IEEE Photonic. Tech. L. 22(18), 1346–1348 (2010).
[Crossref]

Meneghesso, G.

M. Meneghini, N. Trivellin, G. Meneghesso, E. Zanoni, U. Zehnder, and B. Hahn, “A combined electro-optical method for the determination of the recombination parameters in InGaN-based light-emitting diodes,” J. Appl. Phys. 106(11), 114508 (2009).
[Crossref]

Meneghini, M.

M. Meneghini, N. Trivellin, G. Meneghesso, E. Zanoni, U. Zehnder, and B. Hahn, “A combined electro-optical method for the determination of the recombination parameters in InGaN-based light-emitting diodes,” J. Appl. Phys. 106(11), 114508 (2009).
[Crossref]

Meyer, J. R.

I. Vurgaftman and J. R. Meyer, “Band parameters for nitrogen-containing semiconductors,” J. Appl. Phys. 94(6), 3675–3696 (2003).
[Crossref]

Mirjalili, B.

J. Pandey, A. Yu-Te Liao, R. Lingley, B. Mirjalili, Parviz, and B. P. Otis, “A Fully Integrated RF-Powered Contact Lens With a Single Element Display,” IEEE Trans Biomed Circuits Syst 4(6), 454–461 (2010).
[Crossref] [PubMed]

Morgan, F.

I. L. Azevedo, M. G. Morgan, and F. Morgan, “The Transition to Solid-State Lighting,” Proc. IEEE 97(3), 481–510 (2009).
[Crossref]

Morgan, M. G.

I. L. Azevedo, M. G. Morgan, and F. Morgan, “The Transition to Solid-State Lighting,” Proc. IEEE 97(3), 481–510 (2009).
[Crossref]

Mueller, G. O.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, Z. Ling, G. Harbers, and M. G. Craford, “Status and Future of High-Power Light-Emitting Diodes for Solid-State Lighting,” J. Disp. Technol. 3(2), 160–175 (2007).
[Crossref]

Mueller-Mach, R.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, Z. Ling, G. Harbers, and M. G. Craford, “Status and Future of High-Power Light-Emitting Diodes for Solid-State Lighting,” J. Disp. Technol. 3(2), 160–175 (2007).
[Crossref]

Mymrin, V. F.

K. A. Bulashevich, I. Y. Evstratov, V. F. Mymrin, and S. Y. Karpov, “Current spreading and thermal effects in blue LED dice,” Phys. Status Solidi C 4(1), 45–48 (2007).
[Crossref]

Nakamura, S.

J. Piprek and S. Nakamura, “Physics of high-power InGaN/GaN lasers,” IEE Proc., Optoelectron. 149(4), 145–151 (2002).
[Crossref]

Neil, M. A. A.

Z. Gong, E. Gu, S. R. Jin, D. Massoubre, B. Guilhabert, H. X. Zhang, M. D. Dawson, V. Poher, G. T. Kennedy, P. M. W. French, and M. A. A. Neil, “Efficient flip-chip InGaN micro-pixellated light-emitting diode arrays: Promising candidates for micro-displays and colour conversion,” J. Phys. D Appl. Phys. 41(9), 094002 (2008).
[Crossref]

V. Poher, N. Grossman, G. T. Kennedy, K. Nikolic, H. X. Zhang, Z. Gong, E. M. Drakakis, E. Gu, M. D. Dawson, P. M. W. French, P. Degenaar, and M. A. A. Neil, “Micro-LED arrays: a tool for two-dimensional neuron stimulation,” J. Phys. D Appl. Phys. 41(9), 094014 (2008).
[Crossref]

Z. Gong, H. X. Zhang, E. Gu, C. Griffin, M. D. Dawson, V. Poher, G. Kennedy, P. M. W. French, and M. A. A. Neil, “Matrix-addressable micropixellated InGaN light-emitting diodes with uniform emission and increased light output,” IEEE Trans. Electron. Dev. 54(10), 2650–2658 (2007).
[Crossref]

Nikolic, K.

V. Poher, N. Grossman, G. T. Kennedy, K. Nikolic, H. X. Zhang, Z. Gong, E. M. Drakakis, E. Gu, M. D. Dawson, P. M. W. French, P. Degenaar, and M. A. A. Neil, “Micro-LED arrays: a tool for two-dimensional neuron stimulation,” J. Phys. D Appl. Phys. 41(9), 094014 (2008).
[Crossref]

Otis, B. P.

J. Pandey, A. Yu-Te Liao, R. Lingley, B. Mirjalili, Parviz, and B. P. Otis, “A Fully Integrated RF-Powered Contact Lens With a Single Element Display,” IEEE Trans Biomed Circuits Syst 4(6), 454–461 (2010).
[Crossref] [PubMed]

Pandey, J.

J. Pandey, A. Yu-Te Liao, R. Lingley, B. Mirjalili, Parviz, and B. P. Otis, “A Fully Integrated RF-Powered Contact Lens With a Single Element Display,” IEEE Trans Biomed Circuits Syst 4(6), 454–461 (2010).
[Crossref] [PubMed]

Parviz,

J. Pandey, A. Yu-Te Liao, R. Lingley, B. Mirjalili, Parviz, and B. P. Otis, “A Fully Integrated RF-Powered Contact Lens With a Single Element Display,” IEEE Trans Biomed Circuits Syst 4(6), 454–461 (2010).
[Crossref] [PubMed]

Piprek, J.

J. Piprek and S. Nakamura, “Physics of high-power InGaN/GaN lasers,” IEE Proc., Optoelectron. 149(4), 145–151 (2002).
[Crossref]

Poher, V.

Z. Gong, E. Gu, S. R. Jin, D. Massoubre, B. Guilhabert, H. X. Zhang, M. D. Dawson, V. Poher, G. T. Kennedy, P. M. W. French, and M. A. A. Neil, “Efficient flip-chip InGaN micro-pixellated light-emitting diode arrays: Promising candidates for micro-displays and colour conversion,” J. Phys. D Appl. Phys. 41(9), 094002 (2008).
[Crossref]

V. Poher, N. Grossman, G. T. Kennedy, K. Nikolic, H. X. Zhang, Z. Gong, E. M. Drakakis, E. Gu, M. D. Dawson, P. M. W. French, P. Degenaar, and M. A. A. Neil, “Micro-LED arrays: a tool for two-dimensional neuron stimulation,” J. Phys. D Appl. Phys. 41(9), 094014 (2008).
[Crossref]

Z. Gong, H. X. Zhang, E. Gu, C. Griffin, M. D. Dawson, V. Poher, G. Kennedy, P. M. W. French, and M. A. A. Neil, “Matrix-addressable micropixellated InGaN light-emitting diodes with uniform emission and increased light output,” IEEE Trans. Electron. Dev. 54(10), 2650–2658 (2007).
[Crossref]

Rae, B. R.

Shakya, J.

S. X. Jin, J. Shakya, J. Y. Lin, and H. X. Jiang, “Size dependence of III-nitride microdisk light-emitting diode characteristics,” Appl. Phys. Lett. 78(22), 3532–3534 (2001).
[Crossref]

Shchekin, O. B.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, Z. Ling, G. Harbers, and M. G. Craford, “Status and Future of High-Power Light-Emitting Diodes for Solid-State Lighting,” J. Disp. Technol. 3(2), 160–175 (2007).
[Crossref]

Sun, X. W.

Z. G. Ju, W. Liu, Z. H. Zhang, S. T. Tan, Y. Ji, Z. B. Kyaw, X. L. Zhang, S. P. Lu, Y. P. Zhang, B. B. Zhu, N. Hasanov, X. W. Sun, and H. V. Demir, “Improved hole distribution in InGaN/GaN light-emitting diodes with graded thickness quantum barriers,” Appl. Phys. Lett. 102(24), 243504 (2013).
[Crossref]

Z. H. Zhang, S. T. Tan, Z. G. Ju, W. Liu, Y. Ji, Z. Kyaw, Y. Dikme, X. W. Sun, and H. V. Demir, “On the Effect of Step-Doped Quantum Barriers in InGaN/GaN Light Emitting Diodes,” J. Disp. Technol. 9(4), 226–233 (2013).
[Crossref]

Y. Ji, Z. H. Zhang, S. T. Tan, Z. G. Ju, Z. Kyaw, N. Hasanov, W. Liu, X. W. Sun, and H. V. Demir, “Enhanced hole transport in InGaN/GaN multiple quantum well light-emitting diodes with a p-type doped quantum barrier,” Opt. Lett. 38(2), 202–204 (2013).
[Crossref] [PubMed]

Z. H. Zhang, S. T. Tan, W. Liu, Z. G. Ju, K. Zheng, Z. Kyaw, Y. Ji, N. Hasanov, X. W. Sun, and H. V. Demir, “Improved InGaN/GaN light-emitting diodes with a p-GaN/n-GaN/p-GaN/n-GaN/p-GaN current-spreading layer,” Opt. Express 21(4), 4958–4969 (2013).
[PubMed]

S. T. Tan, X. W. Sun, H. V. Demir, and S. P. DenBaars, “Advances in the LED Materials and Architectures for Energy-Saving Solid-State Lighting Toward “Lighting Revolution”,” IEEE Photon. J. 4(2), 613–619 (2012).
[Crossref]

Tan, S. T.

Z. G. Ju, W. Liu, Z. H. Zhang, S. T. Tan, Y. Ji, Z. B. Kyaw, X. L. Zhang, S. P. Lu, Y. P. Zhang, B. B. Zhu, N. Hasanov, X. W. Sun, and H. V. Demir, “Improved hole distribution in InGaN/GaN light-emitting diodes with graded thickness quantum barriers,” Appl. Phys. Lett. 102(24), 243504 (2013).
[Crossref]

Z. H. Zhang, S. T. Tan, Z. G. Ju, W. Liu, Y. Ji, Z. Kyaw, Y. Dikme, X. W. Sun, and H. V. Demir, “On the Effect of Step-Doped Quantum Barriers in InGaN/GaN Light Emitting Diodes,” J. Disp. Technol. 9(4), 226–233 (2013).
[Crossref]

Z. H. Zhang, S. T. Tan, W. Liu, Z. G. Ju, K. Zheng, Z. Kyaw, Y. Ji, N. Hasanov, X. W. Sun, and H. V. Demir, “Improved InGaN/GaN light-emitting diodes with a p-GaN/n-GaN/p-GaN/n-GaN/p-GaN current-spreading layer,” Opt. Express 21(4), 4958–4969 (2013).
[PubMed]

Y. Ji, Z. H. Zhang, S. T. Tan, Z. G. Ju, Z. Kyaw, N. Hasanov, W. Liu, X. W. Sun, and H. V. Demir, “Enhanced hole transport in InGaN/GaN multiple quantum well light-emitting diodes with a p-type doped quantum barrier,” Opt. Lett. 38(2), 202–204 (2013).
[Crossref] [PubMed]

S. T. Tan, X. W. Sun, H. V. Demir, and S. P. DenBaars, “Advances in the LED Materials and Architectures for Energy-Saving Solid-State Lighting Toward “Lighting Revolution”,” IEEE Photon. J. 4(2), 613–619 (2012).
[Crossref]

Tansu, N.

H. P. Zhao, R. A. Arif, Y. K. Ee, and N. Tansu, “Self-Consistent Analysis of Strain-Compensated InGaN-AlGaN Quantum Wells for Lasers and Light-Emitting Diodes,” IEEE J. Quantum Electron. 45(1), 66–78 (2009).
[Crossref]

Trivellin, N.

M. Meneghini, N. Trivellin, G. Meneghesso, E. Zanoni, U. Zehnder, and B. Hahn, “A combined electro-optical method for the determination of the recombination parameters in InGaN-based light-emitting diodes,” J. Appl. Phys. 106(11), 114508 (2009).
[Crossref]

Tsao, J. Y.

R. Haitz and J. Y. Tsao, “Solid-state lighting: ‘The case’ 10 years after and future prospects,” Phys. Status Solidi A 208(1), 17–29 (2011).
[Crossref]

Vurgaftman, I.

I. Vurgaftman and J. R. Meyer, “Band parameters for nitrogen-containing semiconductors,” J. Appl. Phys. 94(6), 3675–3696 (2003).
[Crossref]

Watson, I. M.

G. Zheng, S. Jin, C. Yujie, J. McKendry, D. Massoubre, I. M. Watson, E. Gu, and M. D. Dawson, “Size-dependent light output, spectral shift, and self-heating of 400 nm InGaN light-emitting diodes,” J. Appl. Phys. 107(1), 013103 (2010).
[Crossref]

Yujie, C.

G. Zheng, S. Jin, C. Yujie, J. McKendry, D. Massoubre, I. M. Watson, E. Gu, and M. D. Dawson, “Size-dependent light output, spectral shift, and self-heating of 400 nm InGaN light-emitting diodes,” J. Appl. Phys. 107(1), 013103 (2010).
[Crossref]

Yu-Te Liao, A.

J. Pandey, A. Yu-Te Liao, R. Lingley, B. Mirjalili, Parviz, and B. P. Otis, “A Fully Integrated RF-Powered Contact Lens With a Single Element Display,” IEEE Trans Biomed Circuits Syst 4(6), 454–461 (2010).
[Crossref] [PubMed]

Zanoni, E.

M. Meneghini, N. Trivellin, G. Meneghesso, E. Zanoni, U. Zehnder, and B. Hahn, “A combined electro-optical method for the determination of the recombination parameters in InGaN-based light-emitting diodes,” J. Appl. Phys. 106(11), 114508 (2009).
[Crossref]

Zehnder, U.

M. Meneghini, N. Trivellin, G. Meneghesso, E. Zanoni, U. Zehnder, and B. Hahn, “A combined electro-optical method for the determination of the recombination parameters in InGaN-based light-emitting diodes,” J. Appl. Phys. 106(11), 114508 (2009).
[Crossref]

Zhang, H. X.

Z. Gong, E. Gu, S. R. Jin, D. Massoubre, B. Guilhabert, H. X. Zhang, M. D. Dawson, V. Poher, G. T. Kennedy, P. M. W. French, and M. A. A. Neil, “Efficient flip-chip InGaN micro-pixellated light-emitting diode arrays: Promising candidates for micro-displays and colour conversion,” J. Phys. D Appl. Phys. 41(9), 094002 (2008).
[Crossref]

V. Poher, N. Grossman, G. T. Kennedy, K. Nikolic, H. X. Zhang, Z. Gong, E. M. Drakakis, E. Gu, M. D. Dawson, P. M. W. French, P. Degenaar, and M. A. A. Neil, “Micro-LED arrays: a tool for two-dimensional neuron stimulation,” J. Phys. D Appl. Phys. 41(9), 094014 (2008).
[Crossref]

Z. Gong, H. X. Zhang, E. Gu, C. Griffin, M. D. Dawson, V. Poher, G. Kennedy, P. M. W. French, and M. A. A. Neil, “Matrix-addressable micropixellated InGaN light-emitting diodes with uniform emission and increased light output,” IEEE Trans. Electron. Dev. 54(10), 2650–2658 (2007).
[Crossref]

Zhang, S.

Zhang, X. L.

Z. G. Ju, W. Liu, Z. H. Zhang, S. T. Tan, Y. Ji, Z. B. Kyaw, X. L. Zhang, S. P. Lu, Y. P. Zhang, B. B. Zhu, N. Hasanov, X. W. Sun, and H. V. Demir, “Improved hole distribution in InGaN/GaN light-emitting diodes with graded thickness quantum barriers,” Appl. Phys. Lett. 102(24), 243504 (2013).
[Crossref]

Zhang, Y. P.

Z. G. Ju, W. Liu, Z. H. Zhang, S. T. Tan, Y. Ji, Z. B. Kyaw, X. L. Zhang, S. P. Lu, Y. P. Zhang, B. B. Zhu, N. Hasanov, X. W. Sun, and H. V. Demir, “Improved hole distribution in InGaN/GaN light-emitting diodes with graded thickness quantum barriers,” Appl. Phys. Lett. 102(24), 243504 (2013).
[Crossref]

Zhang, Z. H.

Z. G. Ju, W. Liu, Z. H. Zhang, S. T. Tan, Y. Ji, Z. B. Kyaw, X. L. Zhang, S. P. Lu, Y. P. Zhang, B. B. Zhu, N. Hasanov, X. W. Sun, and H. V. Demir, “Improved hole distribution in InGaN/GaN light-emitting diodes with graded thickness quantum barriers,” Appl. Phys. Lett. 102(24), 243504 (2013).
[Crossref]

Z. H. Zhang, S. T. Tan, Z. G. Ju, W. Liu, Y. Ji, Z. Kyaw, Y. Dikme, X. W. Sun, and H. V. Demir, “On the Effect of Step-Doped Quantum Barriers in InGaN/GaN Light Emitting Diodes,” J. Disp. Technol. 9(4), 226–233 (2013).
[Crossref]

Y. Ji, Z. H. Zhang, S. T. Tan, Z. G. Ju, Z. Kyaw, N. Hasanov, W. Liu, X. W. Sun, and H. V. Demir, “Enhanced hole transport in InGaN/GaN multiple quantum well light-emitting diodes with a p-type doped quantum barrier,” Opt. Lett. 38(2), 202–204 (2013).
[Crossref] [PubMed]

Z. H. Zhang, S. T. Tan, W. Liu, Z. G. Ju, K. Zheng, Z. Kyaw, Y. Ji, N. Hasanov, X. W. Sun, and H. V. Demir, “Improved InGaN/GaN light-emitting diodes with a p-GaN/n-GaN/p-GaN/n-GaN/p-GaN current-spreading layer,” Opt. Express 21(4), 4958–4969 (2013).
[PubMed]

Zhao, H. P.

H. P. Zhao, R. A. Arif, Y. K. Ee, and N. Tansu, “Self-Consistent Analysis of Strain-Compensated InGaN-AlGaN Quantum Wells for Lasers and Light-Emitting Diodes,” IEEE J. Quantum Electron. 45(1), 66–78 (2009).
[Crossref]

Zheng, G.

G. Zheng, S. Jin, C. Yujie, J. McKendry, D. Massoubre, I. M. Watson, E. Gu, and M. D. Dawson, “Size-dependent light output, spectral shift, and self-heating of 400 nm InGaN light-emitting diodes,” J. Appl. Phys. 107(1), 013103 (2010).
[Crossref]

J. J. D. McKendry, R. P. Green, A. E. Kelly, G. Zheng, B. Guilhabert, D. Massoubre, E. Gu, and M. D. Dawson, “High-Speed Visible Light Communications Using Individual Pixels in a Micro Light-Emitting Diode Array,” IEEE Photonic. Tech. L. 22(18), 1346–1348 (2010).
[Crossref]

Zheng, K.

Zhu, B. B.

Z. G. Ju, W. Liu, Z. H. Zhang, S. T. Tan, Y. Ji, Z. B. Kyaw, X. L. Zhang, S. P. Lu, Y. P. Zhang, B. B. Zhu, N. Hasanov, X. W. Sun, and H. V. Demir, “Improved hole distribution in InGaN/GaN light-emitting diodes with graded thickness quantum barriers,” Appl. Phys. Lett. 102(24), 243504 (2013).
[Crossref]

Appl. Phys. Lett. (5)

Z. G. Ju, W. Liu, Z. H. Zhang, S. T. Tan, Y. Ji, Z. B. Kyaw, X. L. Zhang, S. P. Lu, Y. P. Zhang, B. B. Zhu, N. Hasanov, X. W. Sun, and H. V. Demir, “Improved hole distribution in InGaN/GaN light-emitting diodes with graded thickness quantum barriers,” Appl. Phys. Lett. 102(24), 243504 (2013).
[Crossref]

H. W. Choi, M. D. Dawson, P. R. Edwards, and R. W. Martin, “High extraction efficiency InGaN micro-ring light-emitting diodes,” Appl. Phys. Lett. 83(22), 4483–4485 (2003).
[Crossref]

S. X. Jin, J. Shakya, J. Y. Lin, and H. X. Jiang, “Size dependence of III-nitride microdisk light-emitting diode characteristics,” Appl. Phys. Lett. 78(22), 3532–3534 (2001).
[Crossref]

V. Fiorentini, F. Bernardini, and O. Ambacher, “Evidence for nonlinear macroscopic polarization in III-V nitride alloy heterostructures,” Appl. Phys. Lett. 80(7), 1204–1206 (2002).
[Crossref]

S. X. Jin, J. Li, J. Z. Li, J. Y. Lin, and H. X. Jiang, “GaN microdisk light emitting diodes,” Appl. Phys. Lett. 76(5), 631–633 (2000).
[Crossref]

IEE Proc., Optoelectron. (1)

J. Piprek and S. Nakamura, “Physics of high-power InGaN/GaN lasers,” IEE Proc., Optoelectron. 149(4), 145–151 (2002).
[Crossref]

IEEE Electron Device Lett. (1)

H. W. Choi, C. W. Jeon, and M. D. Dawson, “High-resolution 128 x 96 nitride microdisplay,” IEEE Electron Device Lett. 25(5), 277–279 (2004).
[Crossref]

IEEE J. Quantum Electron. (1)

H. P. Zhao, R. A. Arif, Y. K. Ee, and N. Tansu, “Self-Consistent Analysis of Strain-Compensated InGaN-AlGaN Quantum Wells for Lasers and Light-Emitting Diodes,” IEEE J. Quantum Electron. 45(1), 66–78 (2009).
[Crossref]

IEEE J. Sel. Top. Quant. (1)

M. H. Crawford, “LEDs for Solid-State Lighting: Performance Challenges and Recent Advances,” IEEE J. Sel. Top. Quant. 15(4), 1028–1040 (2009).
[Crossref]

IEEE Photon. J. (1)

S. T. Tan, X. W. Sun, H. V. Demir, and S. P. DenBaars, “Advances in the LED Materials and Architectures for Energy-Saving Solid-State Lighting Toward “Lighting Revolution”,” IEEE Photon. J. 4(2), 613–619 (2012).
[Crossref]

IEEE Photonic. Tech. L. (2)

H. W. Choi, C. W. Jeon, and M. D. Dawson, “InGaN microring light-emitting diodes,” IEEE Photonic. Tech. L. 16(1), 33–35 (2004).
[Crossref]

J. J. D. McKendry, R. P. Green, A. E. Kelly, G. Zheng, B. Guilhabert, D. Massoubre, E. Gu, and M. D. Dawson, “High-Speed Visible Light Communications Using Individual Pixels in a Micro Light-Emitting Diode Array,” IEEE Photonic. Tech. L. 22(18), 1346–1348 (2010).
[Crossref]

IEEE Trans Biomed Circuits Syst (1)

J. Pandey, A. Yu-Te Liao, R. Lingley, B. Mirjalili, Parviz, and B. P. Otis, “A Fully Integrated RF-Powered Contact Lens With a Single Element Display,” IEEE Trans Biomed Circuits Syst 4(6), 454–461 (2010).
[Crossref] [PubMed]

IEEE Trans. Electron. Dev. (1)

Z. Gong, H. X. Zhang, E. Gu, C. Griffin, M. D. Dawson, V. Poher, G. Kennedy, P. M. W. French, and M. A. A. Neil, “Matrix-addressable micropixellated InGaN light-emitting diodes with uniform emission and increased light output,” IEEE Trans. Electron. Dev. 54(10), 2650–2658 (2007).
[Crossref]

J. Appl. Phys. (3)

M. Meneghini, N. Trivellin, G. Meneghesso, E. Zanoni, U. Zehnder, and B. Hahn, “A combined electro-optical method for the determination of the recombination parameters in InGaN-based light-emitting diodes,” J. Appl. Phys. 106(11), 114508 (2009).
[Crossref]

G. Zheng, S. Jin, C. Yujie, J. McKendry, D. Massoubre, I. M. Watson, E. Gu, and M. D. Dawson, “Size-dependent light output, spectral shift, and self-heating of 400 nm InGaN light-emitting diodes,” J. Appl. Phys. 107(1), 013103 (2010).
[Crossref]

I. Vurgaftman and J. R. Meyer, “Band parameters for nitrogen-containing semiconductors,” J. Appl. Phys. 94(6), 3675–3696 (2003).
[Crossref]

J. Disp. Technol. (2)

Z. H. Zhang, S. T. Tan, Z. G. Ju, W. Liu, Y. Ji, Z. Kyaw, Y. Dikme, X. W. Sun, and H. V. Demir, “On the Effect of Step-Doped Quantum Barriers in InGaN/GaN Light Emitting Diodes,” J. Disp. Technol. 9(4), 226–233 (2013).
[Crossref]

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, Z. Ling, G. Harbers, and M. G. Craford, “Status and Future of High-Power Light-Emitting Diodes for Solid-State Lighting,” J. Disp. Technol. 3(2), 160–175 (2007).
[Crossref]

J. Lightwave Technol. (1)

J. Phys. D Appl. Phys. (2)

V. Poher, N. Grossman, G. T. Kennedy, K. Nikolic, H. X. Zhang, Z. Gong, E. M. Drakakis, E. Gu, M. D. Dawson, P. M. W. French, P. Degenaar, and M. A. A. Neil, “Micro-LED arrays: a tool for two-dimensional neuron stimulation,” J. Phys. D Appl. Phys. 41(9), 094014 (2008).
[Crossref]

Z. Gong, E. Gu, S. R. Jin, D. Massoubre, B. Guilhabert, H. X. Zhang, M. D. Dawson, V. Poher, G. T. Kennedy, P. M. W. French, and M. A. A. Neil, “Efficient flip-chip InGaN micro-pixellated light-emitting diode arrays: Promising candidates for micro-displays and colour conversion,” J. Phys. D Appl. Phys. 41(9), 094002 (2008).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Status Solidi A (1)

R. Haitz and J. Y. Tsao, “Solid-state lighting: ‘The case’ 10 years after and future prospects,” Phys. Status Solidi A 208(1), 17–29 (2011).
[Crossref]

Phys. Status Solidi C (1)

K. A. Bulashevich, I. Y. Evstratov, V. F. Mymrin, and S. Y. Karpov, “Current spreading and thermal effects in blue LED dice,” Phys. Status Solidi C 4(1), 45–48 (2007).
[Crossref]

Phys. Today (1)

A. Bergh, G. Craford, A. Duggal, and R. Haitz, “The promise and challenge of solid-state lighting,” Phys. Today 54(12), 42–47 (2001).
[Crossref]

Proc. IEEE (1)

I. L. Azevedo, M. G. Morgan, and F. Morgan, “The Transition to Solid-State Lighting,” Proc. IEEE 97(3), 481–510 (2009).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1

J-V diagrams of LTM-LEDs of different sizes for (a) experimental data; and (b) simulated data.

Fig. 2
Fig. 2

(a) Schematic current paths of the LTM-LED and (b) the simplified circuit model for the LTM-LED.

Fig. 3
Fig. 3

(a) J-L and (b) J-L0 behaviour at a fixed voltage bias (11.073V).

Fig. 4
Fig. 4

PD-J diagrams of LTM-LEDs in different sizes: (a) experimental results and (b) simulation results.

Fig. 5
Fig. 5

Schematic view of (a) LTM-LED current spreading layer and mesa margin and (b) the equivalent circuit model for the margin effect.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

R 1 = ρ i T i S 1
r k = ρ NGaN L k S 2
R 2 = ρ NGaN L 0 S 2
J k = V ρ i T i + ρ NGaN L H ×( L k + L 0 ) = V R 0 +aL( L k + L 0 )
J ave = 1 L 0 L J k d L k = V a L 2 ( ln a L 2 +a L 0 L+ R 0 ln a L 0 L+ R 0 )
I 1 I 2 = R 4 + R 5 R 1 + R 2 + R 3

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